Introduction:
Background Information: Since the dawn of humankind, people have been fighting
one another. With sticks and stones at first, then spears, then slings, then
ballistas and catapults until finally, around 400 BC, the trebuchet was born in
ancient China.
200 years later, it was introduced to Europe
and was used until around the 16th century AD. A Trebuchet is a siege engine
used to smash walls by throwing heavy and destructive projectiles long
distances. A trebuchet uses a heavy counterweight attached to a lever arm, to
which a sling is attached to the long end. With the long arm at ground level,
the sling is loaded with a projectile and secured to the ground. When the sling
is released, the counterweight falls with great force and propels the sling and
the projectile into the air, often to great lengths. Some variables to be
considered when building your trebuchet are counterweight, release angle and
arm length.Statement of Problem: The purpose of this investigation
is to research the relationship between the weight of projectiles launched by a
trebuchet and the distance traveled by said projectiles.Review of Literature: We decided to focus
on journals and articles relating to the mass and acceleration of projectiles
and formulas involving the conversation of energy. According to Bob Kibble of
Physics Review (2005), a simple model for a trebuchet is possible by
considering the conservation of energy formula: MgH = 1/2 mv^2+ mgh. Using this
formula, we can predict and calculate the launch velocity if we know the weight
and height of the counterweight when cocked and loaded, the weight and range of
the projectiles and gravity. According to Porter and Tremblay of The Physics
Teacher (2001), the principles of energy conservation can be researched using
the trebuchet. Trebuchets use gravity and weights to launch projectiles into
the air and at enemies. Paul E. Chevedden details the history of the trebuchet
as a siege weapon and it’s architecture, principle of design and the physics of
the trebuchet in his article in The Scientific American (1995).Hypothesis: We believe that the heavier
projectiles will travel a farther distance (m) when launched and will also
launch at a higher velocity (m/s). Velocity is defined as the speed of the
projectile at time of launch. Therefore, if we launch projectiles varying in
mass, then the larger projectiles will travel a farther distance and have a
higher velocity, because the larger mass creates a greater amount of force and
due to the larger mass there is less air friction acting against the
projectile.

Method:
The materials we used to complete this experiment were a trebuchet, 9 1 gallon
milk jugs filled with varying amounts of water, cones to block off the road
from cars, measuring tape and a video camera for documentation. Our setup
looked like this:

We chose to launch the trebuchet in a driveway facing out of a cul du sac
because the trebuchet is extremely difficult to move great distances. Our
procedure was as follows: Load the trebuchet by attaching the projectile to arm
(when cocked, no one is allowed to walk in front or behind trebuchet in case of
1,000 pound counterweight falling and killing you), release arm, measure
distance traveled by projectile, record, repeat until 9 trials with 3 different
masses of projectiles.
We recorded masses of projectiles, height of trebuchet, weight of
counterweight, range traveled by projectiles and height of counterweight when
cocked. The formula we then used is: MgH = ½ mv^2 + mgh. M is mass of
counterweight, g is gravity (9.8 m/s), H is height of the counterweight, m is
mass of projectile and h is height of projectile at launch.

The graph above shows the velocity of each trial. To find the initial velocity
we used the
formula √((d/t)^2+ (gt/2)^2). The d is distance (range), t is time, and g
is gravity (9.8 m/s).

This graph portrays the average velocity of the projectile. As you can see the velocity
decreased as the mass of the projectile decreased. This is a direct
correlation.
There are many places throughout our procedure that mistakes may have been
made. When measuring the range, we may have been off by about one half of a
meter. This would be due to human error. Secondly, we measured the time by
watching the videos from the launches. We may have been incorrect on the time,
due to the lag in reaction time of a human. There is uncertainty in the
velocity due to the uncertainties of our variables.
The formula we used for the uncertainty was: x/v=∆t/t+ ∆d/d+ ∆m/m.
We calculated the uncertainty for each trial and then averaged the
uncertainties. Our average uncertainty for our entire data collection was: +/-
2.94179 m/s. This larger uncertainty, we believe, was due to our larger
uncertainty of the time.

Discussion:
Our data supported our hypothesis! Our graph shows a decrease in velocity as
the mass of the projectile decreases. Our graph and data were very consistent.
We initially planned on using the conservation of energy formula, but we
realized there were too many inconsistencies with the velocities we were
calculating. This happened because there were too many factors reducing the
energy of the projectile, such as arm swing, way the projectile was released,
and the movement of the trebuchet after each launch. Therefore, we decided to
use a standard formula for the projectile velocity upon leaving the Trebuchet.
Which is √ ((d/t)^2+ (gt/2)^2).
There were places of uncertainty, especially in the measurement of the time.
However, our graphs and data support our underlying hypothesis.
If one was interested in doing further research on the trebuchet some other
variables that could be tested are the length of the arm, the mass of the
counterweight and the effect of adding wheels. The wonders of the trebuchet
allow for unlimited experimentation and scientific discovery if one has an open
mind and a good sense of adventure. Happy Trebucheting!